Assignment 7: Forecasting Numeric Data using Regression Models
Lau Wen Jun
2023-04-15
1 Regression Forecasting for Numerical Data
Use the Quality
of Life data (Case06_QoL_Symptom_ChronicIllness) to fit several
different Multiple Linear Regression models predicting clinically
relevant outcomes, e.g., Chronic Disease Score.
Summarize and visualize the data using
summary,str,pairs.panels,ggplot.ql<-read.csv("I:/UBD PB/ZH5102 ML/ass7/Case06_QoL_Symptom_ChronicIllness.csv") summary(ql)## ID INTERVIEWDATE LANGUAGE AGE ## Min. : 171.0 Min. : 0.00 Min. :1.000 Min. :19.00 ## 1st Qu.: 819.8 1st Qu.: 0.00 1st Qu.:1.000 1st Qu.:51.00 ## Median :1427.5 Median : 0.00 Median :1.000 Median :59.00 ## Mean :1472.0 Mean : 19.91 Mean :1.205 Mean :58.56 ## 3rd Qu.:2143.2 3rd Qu.: 0.00 3rd Qu.:1.000 3rd Qu.:66.00 ## Max. :2838.0 Max. :440.00 Max. :2.000 Max. :90.00 ## RACE_ETHNICITY SEX QOL_Q_01 QOL_Q_02 ## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 ## 1st Qu.:3.000 1st Qu.:1.000 1st Qu.:3.000 1st Qu.:3.000 ## Median :3.000 Median :1.000 Median :4.000 Median :3.000 ## Mean :3.615 Mean :1.417 Mean :3.649 Mean :3.407 ## 3rd Qu.:4.000 3rd Qu.:2.000 3rd Qu.:4.000 3rd Qu.:4.000 ## Max. :7.000 Max. :2.000 Max. :6.000 Max. :6.000 ## QOL_Q_03 QOL_Q_04 QOL_Q_05 QOL_Q_06 ## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 ## 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 ## Median :4.000 Median :3.000 Median :3.000 Median :3.000 ## Mean :3.701 Mean :3.022 Mean :3.117 Mean :2.937 ## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 ## Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.000 ## QOL_Q_07 QOL_Q_08 QOL_Q_09 QOL_Q_10 ## Min. :-1.000 Min. :1.000 Min. :1.000 Min. :1.00 ## 1st Qu.: 1.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.00 ## Median : 4.000 Median :3.000 Median :3.000 Median :3.00 ## Mean : 4.108 Mean :2.876 Mean :3.144 Mean :2.92 ## 3rd Qu.: 7.000 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:4.00 ## Max. :10.000 Max. :6.000 Max. :6.000 Max. :6.00 ## MSA_Q_01 MSA_Q_02 MSA_Q_03 MSA_Q_04 ## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 ## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 ## Median :3.000 Median :3.000 Median :2.000 Median :2.000 ## Mean :2.941 Mean :3.035 Mean :2.267 Mean :2.369 ## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000 ## Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.000 ## MSA_Q_05 MSA_Q_06 MSA_Q_07 MSA_Q_08 ## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 ## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 ## Median :1.000 Median :2.000 Median :2.000 Median :1.000 ## Mean :1.862 Mean :2.393 Mean :2.165 Mean :1.453 ## 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:1.000 ## Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.000 ## MSA_Q_09 MSA_Q_10 MSA_Q_11 MSA_Q_12 ## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 ## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 ## Median :2.000 Median :1.000 Median :1.000 Median :1.000 ## Mean :2.144 Mean :1.673 Mean :2.216 Mean :2.009 ## 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:2.000 ## Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.000 ## MSA_Q_13 MSA_Q_14 MSA_Q_15 MSA_Q_16 MSA_Q_17 ## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00 ## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.00 ## Median :1.000 Median :1.000 Median :1.000 Median :1.000 Median :1.00 ## Mean :1.874 Mean :1.968 Mean :1.744 Mean :1.807 Mean :2.06 ## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.00 ## Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.00 ## PH2_Q_01 PH2_Q_02 TOS_Q_01 TOS_Q_02 ## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 ## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000 ## Median :2.000 Median :2.000 Median :2.000 Median :4.000 ## Mean :2.452 Mean :2.343 Mean :2.219 Mean :3.287 ## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:4.000 ## Max. :6.000 Max. :6.000 Max. :5.000 Max. :5.000 ## TOS_Q_03 TOS_Q_04 CHARLSONSCORE CHRONICDISEASESCORE ## Min. :1.000 Min. :1.000 Min. :-9.0000 Min. :-9.0000 ## 1st Qu.:4.000 1st Qu.:5.000 1st Qu.: 0.0000 1st Qu.: 0.7400 ## Median :4.000 Median :5.000 Median : 1.0000 Median : 1.3100 ## Mean :3.768 Mean :4.657 Mean : 0.8718 Mean : 0.8648 ## 3rd Qu.:4.000 3rd Qu.:5.000 3rd Qu.: 1.0000 3rd Qu.: 1.9700 ## Max. :5.000 Max. :6.000 Max. :10.0000 Max. : 4.7600str(ql)## 'data.frame': 2356 obs. of 41 variables: ## $ ID : int 171 171 172 179 180 180 181 182 183 186 ... ## $ INTERVIEWDATE : int 0 427 0 0 0 42 0 0 0 0 ... ## $ LANGUAGE : int 1 1 1 1 1 1 1 1 1 2 ... ## $ AGE : int 49 49 62 44 64 64 52 48 49 78 ... ## $ RACE_ETHNICITY : int 3 3 3 7 3 3 3 3 3 4 ... ## $ SEX : int 2 2 2 2 1 1 2 1 1 1 ... ## $ QOL_Q_01 : int 4 4 3 6 3 3 4 2 3 5 ... ## $ QOL_Q_02 : int 4 3 3 6 2 5 4 1 4 6 ... ## $ QOL_Q_03 : int 4 4 4 6 3 6 4 3 4 4 ... ## $ QOL_Q_04 : int 4 4 2 6 3 6 2 2 5 2 ... ## $ QOL_Q_05 : int 1 5 4 6 2 6 4 3 4 3 ... ## $ QOL_Q_06 : int 4 4 2 6 1 2 4 1 2 4 ... ## $ QOL_Q_07 : int 1 2 5 -1 0 5 8 4 3 7 ... ## $ QOL_Q_08 : int 6 1 3 6 6 6 3 1 2 4 ... ## $ QOL_Q_09 : int 3 4 3 6 2 2 4 2 2 4 ... ## $ QOL_Q_10 : int 3 1 3 6 3 6 3 2 4 3 ... ## $ MSA_Q_01 : int 1 3 2 6 2 3 4 1 1 2 ... ## $ MSA_Q_02 : int 1 1 2 6 1 6 4 3 2 4 ... ## $ MSA_Q_03 : int 2 1 2 6 1 2 3 3 1 2 ... ## $ MSA_Q_04 : int 1 3 2 6 1 2 1 4 1 5 ... ## $ MSA_Q_05 : int 1 1 1 6 1 2 1 6 3 2 ... ## $ MSA_Q_06 : int 1 2 2 6 1 2 1 1 2 2 ... ## $ MSA_Q_07 : int 2 1 3 6 1 1 1 1 1 5 ... ## $ MSA_Q_08 : int 1 1 1 6 1 1 1 1 2 1 ... ## $ MSA_Q_09 : int 1 1 1 6 2 2 4 6 2 1 ... ## $ MSA_Q_10 : int 1 1 1 6 1 1 1 1 1 3 ... ## $ MSA_Q_11 : int 2 3 2 6 1 1 2 1 1 5 ... ## $ MSA_Q_12 : int 1 1 2 6 1 1 2 6 1 3 ... ## $ MSA_Q_13 : int 1 1 1 6 1 6 2 1 4 2 ... ## $ MSA_Q_14 : int 1 1 1 6 1 2 1 1 3 1 ... ## $ MSA_Q_15 : int 2 1 1 6 1 1 3 2 1 3 ... ## $ MSA_Q_16 : int 2 3 5 6 1 2 1 2 1 2 ... ## $ MSA_Q_17 : int 2 1 1 6 1 1 1 1 1 3 ... ## $ PH2_Q_01 : int 3 2 1 5 1 1 3 1 2 3 ... ## $ PH2_Q_02 : int 4 4 1 5 1 2 1 1 4 2 ... ## $ TOS_Q_01 : int 2 2 2 4 1 1 2 2 1 1 ... ## $ TOS_Q_02 : int 1 1 1 4 4 4 1 2 4 4 ... ## $ TOS_Q_03 : int 4 4 4 4 4 4 4 4 4 4 ... ## $ TOS_Q_04 : int 5 5 5 5 5 5 5 5 5 5 ... ## $ CHARLSONSCORE : int 2 2 3 1 0 0 2 8 0 1 ... ## $ CHRONICDISEASESCORE: num 1.6 1.6 1.54 2.97 1.28 1.28 1.31 1.67 2.21 2.51 ...library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.2.3library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.2.3## Warning: package 'readr' was built under R version 4.2.3## Warning: package 'forcats' was built under R version 4.2.3## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ── ## ✔ dplyr 1.1.0 ✔ readr 2.1.4 ## ✔ forcats 1.0.0 ✔ stringr 1.5.0 ## ✔ lubridate 1.9.2 ✔ tibble 3.1.8 ## ✔ purrr 1.0.1 ✔ tidyr 1.3.0 ## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ── ## ✖ dplyr::filter() masks stats::filter() ## ✖ dplyr::lag() masks stats::lag() ## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errorslibrary(dplyr) ql$LANGUAGE<-as.factor(recode(ql$LANGUAGE,"1" = "ENGLISH","2" = "SPANISH")) ql$SEX<-as.factor(recode(ql$SEX,"1" = "FEMALE","2" = "MALE")) ql$RACE_ETHNICITY<-as.factor(recode(ql$RACE_ETHNICITY,"1" = "AI-ALN","2" = "ASIAN","3" = "BLACK","4" = "HISPANIC","5"= "NHPIS","6" = "WHITE","7" = "UNKNOWN")) ql$QOL_Q_07<-as.integer(ifelse(ql$QOL_Q_07<0, "NA", ql$QOL_Q_07))## Warning: NAs introduced by coercionql$CHARLSONSCORE<-as.integer(ifelse(ql$CHARLSONSCORE<0, "NA", ql$CHARLSONSCORE))## Warning: NAs introduced by coercionql$CHRONICDISEASESCORE<-as.integer(ifelse(ql$CHRONICDISEASESCORE<0, "NA", ql$CHRONICDISEASESCORE))## Warning: NAs introduced by coercionql <- na.omit(ql[,c(-1,-2)]) library(psych)## Warning: package 'psych' was built under R version 4.2.3## ## Attaching package: 'psych' ## ## The following objects are masked from 'package:ggplot2': ## ## %+%, alphapairs.panels(ql[,c(2,38:39)])
library(ggplot2) agep<-ggplot(data=ql, aes(x=AGE)) + geom_bar(stat="bin", width=0.7, fill="steelblue") agep## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
csp<-ggplot(data=ql, aes(x=CHARLSONSCORE)) + geom_bar(stat="bin", width=0.7, fill="steelblue") csp## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
cdsp<-ggplot(data=ql, aes(x=CHRONICDISEASESCORE)) + geom_bar(stat="bin", width=0.7, fill="steelblue") cdsp## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
library(GGally)## Warning: package 'GGally' was built under R version 4.2.3## Registered S3 method overwritten by 'GGally': ## method from ## +.gg ggplot2g_position <- ggpairs(data=ql[,c(2,4,38:39)], title="Quality of Life by Gender", mapping=ggplot2::aes(colour = SEX), lower=list(combo=wrap("facethist",binwidth=1))) g_position
```
Report paired correlations for numeric data and try to visualize these (e.g., heatmap, pairs plot, etc.)
cor(ql[,c(2,38:39)])## AGE CHARLSONSCORE CHRONICDISEASESCORE ## AGE 1.00000000 0.08466444 0.09067902 ## CHARLSONSCORE 0.08466444 1.00000000 0.19488969 ## CHRONICDISEASESCORE 0.09067902 0.19488969 1.00000000my_colors <- colorRampPalette(c("cyan", "blue","navyblue", "deeppink3")) heatmap(cor(ql[,c(2,38:39)]),Rowv = NA, Colv = NA, col=my_colors(256))
library(plotly)## Warning: package 'plotly' was built under R version 4.2.3## ## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2': ## ## last_plot## The following object is masked from 'package:stats': ## ## filter## The following object is masked from 'package:graphics': ## ## layoutplot_ly(ql) %>% add_trace(type = 'splom', dimensions = list( list(label='Age', values=~AGE), list(label='Charlson Score', values=~CHARLSONSCORE), list(label='Chronic Disease Score', values=~CHRONICDISEASESCORE)), marker = list(color = as.integer(ql$SEX), size = 7, line = list(width = 1, color = 'rgb(230,230,230)') ) ) %>% layout(title= 'QL Pairs Plot', hovermode='closest', dragmode= 'select', plot_bgcolor='rgba(240,240,240, 0.95)')Examine potential dependencies of the predictors and the dependent response variables
# Low correlation coefficient indicate independencies or no multicollinearity among the numerical variable. # Response variables are identified to be Chronic Disease Score or Charlson Score as they are the outcome/ output influenced by demographic predictors(Age, Gender, etc).Fit a Multiple Linear Regression model, report the results, and explain the summary, residuals, effect-size coefficients, and the coefficient of determination, \(R^2\).
fit <- lm(CHRONICDISEASESCORE ~ ., data=ql) summary(fit)## ## Call: ## lm(formula = CHRONICDISEASESCORE ~ ., data = ql) ## ## Residuals: ## Min 1Q Median 3Q Max ## -2.07812 -0.66297 -0.00553 0.41054 2.88359 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 1.815e-01 2.218e-01 0.818 0.413246 ## LANGUAGESPANISH -9.785e-02 6.870e-02 -1.424 0.154506 ## AGE 5.211e-03 1.583e-03 3.293 0.001009 ** ## RACE_ETHNICITYASIAN -1.012e-01 1.694e-01 -0.598 0.550183 ## RACE_ETHNICITYBLACK -1.451e-01 1.561e-01 -0.930 0.352638 ## RACE_ETHNICITYHISPANIC 1.233e-01 1.534e-01 0.804 0.421418 ## RACE_ETHNICITYNHPIS -1.365e-02 3.592e-01 -0.038 0.969692 ## RACE_ETHNICITYUNKNOWN 8.122e-02 1.709e-01 0.475 0.634635 ## RACE_ETHNICITYWHITE -7.069e-02 1.642e-01 -0.431 0.666853 ## SEXMALE -2.463e-02 3.905e-02 -0.631 0.528230 ## QOL_Q_01 -1.204e-02 2.360e-02 -0.510 0.610119 ## QOL_Q_02 7.079e-02 2.120e-02 3.340 0.000855 *** ## QOL_Q_03 1.674e-02 2.484e-02 0.674 0.500336 ## QOL_Q_04 -1.785e-02 1.902e-02 -0.938 0.348123 ## QOL_Q_05 1.507e-02 1.921e-02 0.784 0.432859 ## QOL_Q_06 3.537e-02 1.695e-02 2.086 0.037091 * ## QOL_Q_07 3.027e-02 7.965e-03 3.801 0.000149 *** ## QOL_Q_08 -1.084e-02 1.950e-02 -0.556 0.578522 ## QOL_Q_09 -3.519e-02 2.067e-02 -1.703 0.088799 . ## QOL_Q_10 1.267e-03 1.734e-02 0.073 0.941761 ## MSA_Q_01 1.149e-02 1.728e-02 0.665 0.506358 ## MSA_Q_02 1.576e-03 1.694e-02 0.093 0.925879 ## MSA_Q_03 -1.145e-02 1.531e-02 -0.748 0.454601 ## MSA_Q_04 3.190e-03 1.469e-02 0.217 0.828171 ## MSA_Q_05 -7.064e-03 1.590e-02 -0.444 0.656881 ## MSA_Q_06 3.581e-02 1.562e-02 2.293 0.021937 * ## MSA_Q_07 -3.610e-03 1.451e-02 -0.249 0.803541 ## MSA_Q_08 -2.177e-02 1.847e-02 -1.179 0.238545 ## MSA_Q_09 4.984e-04 1.522e-02 0.033 0.973878 ## MSA_Q_10 9.468e-03 1.555e-02 0.609 0.542755 ## MSA_Q_11 -9.008e-03 1.165e-02 -0.773 0.439569 ## MSA_Q_12 1.211e-02 1.396e-02 0.867 0.386050 ## MSA_Q_13 2.348e-02 1.493e-02 1.573 0.115810 ## MSA_Q_14 -3.481e-05 1.576e-02 -0.002 0.998237 ## MSA_Q_15 -2.012e-02 1.525e-02 -1.319 0.187279 ## MSA_Q_16 -3.469e-03 1.447e-02 -0.240 0.810561 ## MSA_Q_17 1.160e-02 1.394e-02 0.832 0.405433 ## PH2_Q_01 6.986e-03 1.721e-02 0.406 0.684843 ## PH2_Q_02 3.210e-02 1.889e-02 1.699 0.089451 . ## TOS_Q_01 -2.149e-02 1.967e-02 -1.093 0.274600 ## TOS_Q_02 -8.441e-03 1.465e-02 -0.576 0.564599 ## TOS_Q_03 1.124e-02 5.983e-02 0.188 0.850949 ## TOS_Q_04 -1.237e-02 4.699e-02 -0.263 0.792354 ## CHARLSONSCORE 1.163e-01 1.440e-02 8.079 1.14e-15 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.7918 on 1944 degrees of freedom ## Multiple R-squared: 0.1077, Adjusted R-squared: 0.08798 ## F-statistic: 5.458 on 43 and 1944 DF, p-value: < 2.2e-16#F Statistics is significant, at least one predictor is related to response variable. # The Significant variables are AGE, QOL_Q_02, QOL_Q_06 ,QOL_Q_07, MSA_Q_06 & CHARLSONSCORE. # Every per unit increase by AGE resulted in 0.0052 increase in CHRONICDISEASESCORE. # Every per unit increase by QOL_Q_02, QOL_Q_06 ,QOL_Q_07 and MSA_Q_06 resulted in 0.071,0.035, 0.030 and 0.036 increase in CHRONICDISEASESCORE respectively. # Every per unit increase by CHARLSONSCORE resulted in 0.12 increase in CHRONICDISEASESCORE. # The range of actual and predicted value have a median of -0.006 & range of 5.03451 (-2.08 to 2.88) # Rsq of 0.09 indicates a weak relationship between the independent and dependent variables.Draw model diagnostic plots, at least QQ plot, residuals plot and leverage plot (half norm plot)
# Residual Plot plot_ly(x=fit$fitted.values, y=fit$residuals, type="scatter", mode="markers") %>% layout(title="LM: Fitted-values vs. Model-Residuals", xaxis=list(title="Fitted"), yaxis = list(title="Residuals"))QQ <- qqplot(fit$fitted.values, fit$residuals, plot.it=FALSE) plot_ly() %>% add_markers(x=~QQ$x, y=~QQ$y, name="Quantiles Scatter", type="scatter", mode="markers") %>% add_trace(x = ~c(0.2,2.4), y = ~c(-2,3), type="scatter", mode="lines", line = list(color = "red", width = 4), name="Line", showlegend=F) %>% layout(title='Quantile plot', xaxis = list(title="Fitted"), yaxis = list(title="Residuals"), legend = list(orientation = 'h'))library(faraway)## Warning: package 'faraway' was built under R version 4.2.3## ## Attaching package: 'faraway'## The following object is masked from 'package:GGally': ## ## happy## The following object is masked from 'package:psych': ## ## logithalfnorm(lm.influence(fit)$hat, nlab = 2, ylab="Leverages")
ql[c(255,783),]## LANGUAGE AGE RACE_ETHNICITY SEX QOL_Q_01 QOL_Q_02 QOL_Q_03 QOL_Q_04 ## 296 ENGLISH 40 NHPIS MALE 2 2 2 1 ## 923 ENGLISH 58 NHPIS MALE 3 4 3 3 ## QOL_Q_05 QOL_Q_06 QOL_Q_07 QOL_Q_08 QOL_Q_09 QOL_Q_10 MSA_Q_01 MSA_Q_02 ## 296 2 1 1 1 2 2 2 2 ## 923 3 2 1 1 3 1 1 2 ## MSA_Q_03 MSA_Q_04 MSA_Q_05 MSA_Q_06 MSA_Q_07 MSA_Q_08 MSA_Q_09 MSA_Q_10 ## 296 1 2 1 1 1 6 1 2 ## 923 2 1 1 1 1 1 1 1 ## MSA_Q_11 MSA_Q_12 MSA_Q_13 MSA_Q_14 MSA_Q_15 MSA_Q_16 MSA_Q_17 PH2_Q_01 ## 296 1 3 2 1 1 1 1 5 ## 923 1 1 1 1 6 6 1 1 ## PH2_Q_02 TOS_Q_01 TOS_Q_02 TOS_Q_03 TOS_Q_04 CHARLSONSCORE ## 296 1 1 4 4 5 0 ## 923 1 1 4 4 5 1 ## CHRONICDISEASESCORE ## 296 0 ## 923 2Predict outcomes for new data
# Categorize by age 30 above and below. ql$AGE<-ifelse(ql$AGE>=30, 1, 0) # Include only the significant and demographic variables of previous data. fit2<-lm(CHRONICDISEASESCORE ~ ., data=ql[,c(1:4,6,10:11,20,38:39)]) summary(fit2)## ## Call: ## lm(formula = CHRONICDISEASESCORE ~ ., data = ql[, c(1:4, 6, 10:11, ## 20, 38:39)]) ## ## Residuals: ## Min 1Q Median 3Q Max ## -2.0525 -0.6765 -0.0041 0.3924 2.9009 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -0.082160 0.211861 -0.388 0.698205 ## LANGUAGESPANISH -0.109363 0.067368 -1.623 0.104671 ## AGE 0.484972 0.136504 3.553 0.000390 *** ## RACE_ETHNICITYASIAN -0.079565 0.167137 -0.476 0.634093 ## RACE_ETHNICITYBLACK -0.130269 0.153212 -0.850 0.395288 ## RACE_ETHNICITYHISPANIC 0.126918 0.151539 0.838 0.402396 ## RACE_ETHNICITYNHPIS -0.054760 0.355878 -0.154 0.877727 ## RACE_ETHNICITYUNKNOWN 0.085692 0.168143 0.510 0.610364 ## RACE_ETHNICITYWHITE -0.072733 0.161392 -0.451 0.652284 ## SEXMALE -0.044426 0.036931 -1.203 0.229150 ## QOL_Q_02 0.066253 0.017335 3.822 0.000136 *** ## QOL_Q_06 0.034672 0.015321 2.263 0.023743 * ## QOL_Q_07 0.029484 0.006553 4.499 7.22e-06 *** ## MSA_Q_06 0.037547 0.013629 2.755 0.005922 ** ## CHARLSONSCORE 0.116103 0.014109 8.229 3.38e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.7895 on 1973 degrees of freedom ## Multiple R-squared: 0.09968, Adjusted R-squared: 0.09329 ## F-statistic: 15.6 on 14 and 1973 DF, p-value: < 2.2e-16# Significant Variables are similar to previous data. # Coefficients of AGE have increased drastically compare with previous data.Try to improve the model performance using
stepfunction based on AIC and BIC.step(fit2,direction = "backward")## Start: AIC=-925.04 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + SEX + ## QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## - SEX 1 0.902 1230.5 -925.58 ## <none> 1229.7 -925.04 ## - LANGUAGE 1 1.642 1231.3 -924.38 ## - QOL_Q_06 1 3.192 1232.8 -921.88 ## - MSA_Q_06 1 4.731 1234.4 -919.40 ## - RACE_ETHNICITY 6 11.217 1240.9 -918.98 ## - AGE 1 7.867 1237.5 -914.36 ## - QOL_Q_02 1 9.104 1238.8 -912.37 ## - QOL_Q_07 1 12.616 1242.3 -906.74 ## - CHARLSONSCORE 1 42.206 1271.9 -859.95 ## ## Step: AIC=-925.58 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + QOL_Q_02 + ## QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## <none> 1230.5 -925.58 ## - LANGUAGE 1 1.468 1232.0 -925.21 ## - QOL_Q_06 1 3.181 1233.7 -922.45 ## - RACE_ETHNICITY 6 10.758 1241.3 -920.27 ## - MSA_Q_06 1 4.713 1235.3 -919.98 ## - AGE 1 8.530 1239.1 -913.85 ## - QOL_Q_02 1 8.930 1239.5 -913.21 ## - QOL_Q_07 1 13.691 1244.2 -905.58 ## - CHARLSONSCORE 1 41.465 1272.0 -861.70## ## Call: ## lm(formula = CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + ## QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE, ## data = ql[, c(1:4, 6, 10:11, 20, 38:39)]) ## ## Coefficients: ## (Intercept) LANGUAGESPANISH AGE ## -0.11835 -0.10306 0.50221 ## RACE_ETHNICITYASIAN RACE_ETHNICITYBLACK RACE_ETHNICITYHISPANIC ## -0.07789 -0.12875 0.12157 ## RACE_ETHNICITYNHPIS RACE_ETHNICITYUNKNOWN RACE_ETHNICITYWHITE ## -0.05902 0.08367 -0.07806 ## QOL_Q_02 QOL_Q_06 QOL_Q_07 ## 0.06558 0.03461 0.03047 ## MSA_Q_06 CHARLSONSCORE ## 0.03748 0.11466step(fit2,direction = "forward") ## retain all variables## Start: AIC=-925.04 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + SEX + ## QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE## ## Call: ## lm(formula = CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + ## SEX + QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE, ## data = ql[, c(1:4, 6, 10:11, 20, 38:39)]) ## ## Coefficients: ## (Intercept) LANGUAGESPANISH AGE ## -0.08216 -0.10936 0.48497 ## RACE_ETHNICITYASIAN RACE_ETHNICITYBLACK RACE_ETHNICITYHISPANIC ## -0.07956 -0.13027 0.12692 ## RACE_ETHNICITYNHPIS RACE_ETHNICITYUNKNOWN RACE_ETHNICITYWHITE ## -0.05476 0.08569 -0.07273 ## SEXMALE QOL_Q_02 QOL_Q_06 ## -0.04443 0.06625 0.03467 ## QOL_Q_07 MSA_Q_06 CHARLSONSCORE ## 0.02948 0.03755 0.11610step(fit2,direction = "both") ## Identical to backward## Start: AIC=-925.04 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + SEX + ## QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## - SEX 1 0.902 1230.5 -925.58 ## <none> 1229.7 -925.04 ## - LANGUAGE 1 1.642 1231.3 -924.38 ## - QOL_Q_06 1 3.192 1232.8 -921.88 ## - MSA_Q_06 1 4.731 1234.4 -919.40 ## - RACE_ETHNICITY 6 11.217 1240.9 -918.98 ## - AGE 1 7.867 1237.5 -914.36 ## - QOL_Q_02 1 9.104 1238.8 -912.37 ## - QOL_Q_07 1 12.616 1242.3 -906.74 ## - CHARLSONSCORE 1 42.206 1271.9 -859.95 ## ## Step: AIC=-925.58 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + QOL_Q_02 + ## QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## <none> 1230.5 -925.58 ## - LANGUAGE 1 1.468 1232.0 -925.21 ## + SEX 1 0.902 1229.7 -925.04 ## - QOL_Q_06 1 3.181 1233.7 -922.45 ## - RACE_ETHNICITY 6 10.758 1241.3 -920.27 ## - MSA_Q_06 1 4.713 1235.3 -919.98 ## - AGE 1 8.530 1239.1 -913.85 ## - QOL_Q_02 1 8.930 1239.5 -913.21 ## - QOL_Q_07 1 13.691 1244.2 -905.58 ## - CHARLSONSCORE 1 41.465 1272.0 -861.70## ## Call: ## lm(formula = CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + ## QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE, ## data = ql[, c(1:4, 6, 10:11, 20, 38:39)]) ## ## Coefficients: ## (Intercept) LANGUAGESPANISH AGE ## -0.11835 -0.10306 0.50221 ## RACE_ETHNICITYASIAN RACE_ETHNICITYBLACK RACE_ETHNICITYHISPANIC ## -0.07789 -0.12875 0.12157 ## RACE_ETHNICITYNHPIS RACE_ETHNICITYUNKNOWN RACE_ETHNICITYWHITE ## -0.05902 0.08367 -0.07806 ## QOL_Q_02 QOL_Q_06 QOL_Q_07 ## 0.06558 0.03461 0.03047 ## MSA_Q_06 CHARLSONSCORE ## 0.03748 0.11466fit3<-step(fit2,k=2,direction = "backward")## Start: AIC=-925.04 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + SEX + ## QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## - SEX 1 0.902 1230.5 -925.58 ## <none> 1229.7 -925.04 ## - LANGUAGE 1 1.642 1231.3 -924.38 ## - QOL_Q_06 1 3.192 1232.8 -921.88 ## - MSA_Q_06 1 4.731 1234.4 -919.40 ## - RACE_ETHNICITY 6 11.217 1240.9 -918.98 ## - AGE 1 7.867 1237.5 -914.36 ## - QOL_Q_02 1 9.104 1238.8 -912.37 ## - QOL_Q_07 1 12.616 1242.3 -906.74 ## - CHARLSONSCORE 1 42.206 1271.9 -859.95 ## ## Step: AIC=-925.58 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + QOL_Q_02 + ## QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## <none> 1230.5 -925.58 ## - LANGUAGE 1 1.468 1232.0 -925.21 ## - QOL_Q_06 1 3.181 1233.7 -922.45 ## - RACE_ETHNICITY 6 10.758 1241.3 -920.27 ## - MSA_Q_06 1 4.713 1235.3 -919.98 ## - AGE 1 8.530 1239.1 -913.85 ## - QOL_Q_02 1 8.930 1239.5 -913.21 ## - QOL_Q_07 1 13.691 1244.2 -905.58 ## - CHARLSONSCORE 1 41.465 1272.0 -861.70step(fit2,k=log(nrow(ql)),direction = "backward")## Start: AIC=-841.11 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + SEX + ## QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## - RACE_ETHNICITY 6 11.217 1240.9 -868.63 ## - SEX 1 0.902 1230.5 -847.25 ## - LANGUAGE 1 1.642 1231.3 -846.05 ## - QOL_Q_06 1 3.192 1232.8 -843.55 ## <none> 1229.7 -841.11 ## - MSA_Q_06 1 4.731 1234.4 -841.07 ## - AGE 1 7.867 1237.5 -836.03 ## - QOL_Q_02 1 9.104 1238.8 -834.04 ## - QOL_Q_07 1 12.616 1242.3 -828.42 ## - CHARLSONSCORE 1 42.206 1271.9 -781.62 ## ## Step: AIC=-868.63 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + SEX + QOL_Q_02 + QOL_Q_06 + ## QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## - SEX 1 0.443 1241.3 -875.52 ## - LANGUAGE 1 2.531 1243.4 -872.18 ## - QOL_Q_06 1 2.744 1243.6 -871.83 ## - MSA_Q_06 1 4.419 1245.3 -869.16 ## <none> 1240.9 -868.63 ## - AGE 1 7.183 1248.0 -864.75 ## - QOL_Q_02 1 9.834 1250.7 -860.53 ## - QOL_Q_07 1 12.201 1253.1 -856.77 ## - CHARLSONSCORE 1 42.535 1283.4 -809.22 ## ## Step: AIC=-875.52 ## CHRONICDISEASESCORE ~ LANGUAGE + AGE + QOL_Q_02 + QOL_Q_06 + ## QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## - LANGUAGE 1 2.590 1243.9 -878.97 ## - QOL_Q_06 1 2.751 1244.1 -878.71 ## - MSA_Q_06 1 4.399 1245.7 -876.08 ## <none> 1241.3 -875.52 ## - AGE 1 7.685 1249.0 -870.84 ## - QOL_Q_02 1 9.698 1251.0 -867.64 ## - QOL_Q_07 1 13.009 1254.3 -862.38 ## - CHARLSONSCORE 1 42.102 1283.4 -816.80 ## ## Step: AIC=-878.97 ## CHRONICDISEASESCORE ~ AGE + QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + ## MSA_Q_06 + CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## - QOL_Q_06 1 3.128 1247.0 -881.57 ## - MSA_Q_06 1 4.516 1248.4 -879.36 ## <none> 1243.9 -878.97 ## - AGE 1 7.594 1251.5 -874.46 ## - QOL_Q_02 1 10.116 1254.0 -870.46 ## - QOL_Q_07 1 12.111 1256.0 -867.30 ## - CHARLSONSCORE 1 42.776 1286.7 -819.35 ## ## Step: AIC=-881.57 ## CHRONICDISEASESCORE ~ AGE + QOL_Q_02 + QOL_Q_07 + MSA_Q_06 + ## CHARLSONSCORE ## ## Df Sum of Sq RSS AIC ## <none> 1247.0 -881.57 ## - MSA_Q_06 1 5.283 1252.3 -880.76 ## - AGE 1 8.191 1255.2 -876.15 ## - QOL_Q_02 1 14.145 1261.2 -866.74 ## - QOL_Q_07 1 17.065 1264.1 -862.14 ## - CHARLSONSCORE 1 46.047 1293.1 -817.08## ## Call: ## lm(formula = CHRONICDISEASESCORE ~ AGE + QOL_Q_02 + QOL_Q_07 + ## MSA_Q_06 + CHARLSONSCORE, data = ql[, c(1:4, 6, 10:11, 20, ## 38:39)]) ## ## Coefficients: ## (Intercept) AGE QOL_Q_02 QOL_Q_07 MSA_Q_06 ## -0.13947 0.48938 0.07956 0.03243 0.03934 ## CHARLSONSCORE ## 0.11983# fit3: AIC has lower value than BIC, thus better fit model. summary(fit3)## ## Call: ## lm(formula = CHRONICDISEASESCORE ~ LANGUAGE + AGE + RACE_ETHNICITY + ## QOL_Q_02 + QOL_Q_06 + QOL_Q_07 + MSA_Q_06 + CHARLSONSCORE, ## data = ql[, c(1:4, 6, 10:11, 20, 38:39)]) ## ## Residuals: ## Min 1Q Median 3Q Max ## -2.01931 -0.67205 -0.00315 0.38513 2.91531 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -0.118348 0.209738 -0.564 0.572637 ## LANGUAGESPANISH -0.103063 0.067172 -1.534 0.125112 ## AGE 0.502214 0.135765 3.699 0.000222 *** ## RACE_ETHNICITYASIAN -0.077889 0.167150 -0.466 0.641278 ## RACE_ETHNICITYBLACK -0.128755 0.153224 -0.840 0.400839 ## RACE_ETHNICITYHISPANIC 0.121570 0.151491 0.802 0.422364 ## RACE_ETHNICITYNHPIS -0.059023 0.355901 -0.166 0.868299 ## RACE_ETHNICITYUNKNOWN 0.083667 0.168154 0.498 0.618848 ## RACE_ETHNICITYWHITE -0.078055 0.161349 -0.484 0.628606 ## QOL_Q_02 0.065581 0.017328 3.785 0.000158 *** ## QOL_Q_06 0.034615 0.015323 2.259 0.023992 * ## QOL_Q_07 0.030472 0.006502 4.686 2.97e-06 *** ## MSA_Q_06 0.037479 0.013630 2.750 0.006019 ** ## CHARLSONSCORE 0.114663 0.014059 8.156 6.10e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.7895 on 1974 degrees of freedom ## Multiple R-squared: 0.09902, Adjusted R-squared: 0.09309 ## F-statistic: 16.69 on 13 and 1974 DF, p-value: < 2.2e-16#F Statistics is significant, at least one predictor is related to response variable. # Identical significant variables as previous new data. # Every per unit increase by AGE resulted in a 0.502 increase in CHRONICDISEASESCORE. # Every per unit increase by QOL_Q_02, QOL_Q_06, QOL_Q_07 and MSA_Q_06 resulted in 0.066,0.035, 0.030 and 0.037 increase in CHRONICDISEASESCORE respectively. # Every per unit increase by CHARLSONSCORE resulted in 0.114 increase in CHRONICDISEASESCORE. # The range of actual and predicted value have a median of -0.003 & range of 5 (-2.02 to 2.92) # Rsq of 0.09 indicates a weak relationship between the independent and dependent variables.Fit a regression tree model and compare with OLS model.
set.seed(1234) train_index <- sample(seq_len(nrow(ql)), size = 0.75*nrow(ql)) ql_train<-ql[train_index, ] ql_test<-ql[-train_index, ] summary(lm(CHRONICDISEASESCORE~., data=ql_train))## ## Call: ## lm(formula = CHRONICDISEASESCORE ~ ., data = ql_train) ## ## Residuals: ## Min 1Q Median 3Q Max ## -2.14883 -0.66731 -0.00825 0.38780 2.90044 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -0.0257307 0.2799454 -0.092 0.92678 ## LANGUAGESPANISH -0.0770432 0.0790493 -0.975 0.32991 ## AGE 0.4571456 0.1598073 2.861 0.00429 ** ## RACE_ETHNICITYASIAN -0.0597598 0.1931044 -0.309 0.75701 ## RACE_ETHNICITYBLACK -0.0907984 0.1774578 -0.512 0.60897 ## RACE_ETHNICITYHISPANIC 0.1616797 0.1738576 0.930 0.35255 ## RACE_ETHNICITYNHPIS -0.0920479 0.4360994 -0.211 0.83286 ## RACE_ETHNICITYUNKNOWN 0.1110545 0.1964899 0.565 0.57203 ## RACE_ETHNICITYWHITE -0.0246570 0.1864585 -0.132 0.89481 ## SEXMALE -0.0598108 0.0449652 -1.330 0.18368 ## QOL_Q_01 -0.0004913 0.0279118 -0.018 0.98596 ## QOL_Q_02 0.0733640 0.0259839 2.823 0.00482 ** ## QOL_Q_03 0.0005606 0.0294120 0.019 0.98480 ## QOL_Q_04 -0.0231842 0.0225800 -1.027 0.30471 ## QOL_Q_05 0.0221581 0.0226104 0.980 0.32725 ## QOL_Q_06 0.0579824 0.0200179 2.897 0.00383 ** ## QOL_Q_07 0.0213856 0.0091307 2.342 0.01931 * ## QOL_Q_08 -0.0131849 0.0229508 -0.574 0.56573 ## QOL_Q_09 -0.0518087 0.0250643 -2.067 0.03891 * ## QOL_Q_10 -0.0022962 0.0199863 -0.115 0.90855 ## MSA_Q_01 0.0415030 0.0200249 2.073 0.03839 * ## MSA_Q_02 0.0091648 0.0197516 0.464 0.64272 ## MSA_Q_03 -0.0103725 0.0174358 -0.595 0.55201 ## MSA_Q_04 0.0027707 0.0170532 0.162 0.87095 ## MSA_Q_05 -0.0014824 0.0185146 -0.080 0.93619 ## MSA_Q_06 0.0275880 0.0181914 1.517 0.12960 ## MSA_Q_07 -0.0086310 0.0168410 -0.513 0.60838 ## MSA_Q_08 -0.0074402 0.0223500 -0.333 0.73926 ## MSA_Q_09 -0.0060522 0.0179840 -0.337 0.73652 ## MSA_Q_10 -0.0031801 0.0187496 -0.170 0.86534 ## MSA_Q_11 -0.0062949 0.0136786 -0.460 0.64544 ## MSA_Q_12 0.0039744 0.0164366 0.242 0.80897 ## MSA_Q_13 0.0159564 0.0179037 0.891 0.37295 ## MSA_Q_14 -0.0017463 0.0188061 -0.093 0.92603 ## MSA_Q_15 -0.0117920 0.0182987 -0.644 0.51941 ## MSA_Q_16 -0.0108404 0.0172565 -0.628 0.52997 ## MSA_Q_17 0.0143954 0.0166083 0.867 0.38622 ## PH2_Q_01 0.0159562 0.0205568 0.776 0.43776 ## PH2_Q_02 0.0140759 0.0225818 0.623 0.53317 ## TOS_Q_01 0.0005752 0.0230805 0.025 0.98012 ## TOS_Q_02 -0.0281588 0.0168897 -1.667 0.09569 . ## TOS_Q_03 -0.0161438 0.0704074 -0.229 0.81868 ## TOS_Q_04 0.0193578 0.0554551 0.349 0.72709 ## CHARLSONSCORE 0.1182002 0.0166371 7.105 1.89e-12 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.7951 on 1447 degrees of freedom ## Multiple R-squared: 0.1145, Adjusted R-squared: 0.08822 ## F-statistic: 4.353 on 43 and 1447 DF, p-value: < 2.2e-16## Train data has identical significant variable when compared with unsplit new data. library(rpart)## ## Attaching package: 'rpart'## The following object is masked from 'package:faraway': ## ## solderql.rpart<-rpart(CHRONICDISEASESCORE~., data=ql_train) ql.rpart## n= 1491 ## ## node), split, n, deviance, yval ## * denotes terminal node ## ## 1) root 1491 1033.1160 0.9644534 ## 2) CHARLSONSCORE< 0.5 560 267.7839 0.6053571 ## 4) MSA_Q_02< 3.5 336 127.9732 0.4910714 * ## 5) MSA_Q_02>=3.5 224 128.8393 0.7767857 * ## 3) CHARLSONSCORE>=0.5 931 649.6842 1.1804510 ## 6) MSA_Q_02< 3.5 602 339.9286 1.0714290 * ## 7) MSA_Q_02>=3.5 329 289.5076 1.3799390 *library(rpart.plot)## Warning: package 'rpart.plot' was built under R version 4.2.3rpart.plot(ql.rpart, digits=4)
ql.p<-predict(ql.rpart, ql_test) summary(ql.p)## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 0.4911 0.7768 1.0714 0.9779 1.0714 1.3799cor(ql.p, ql_test$CHRONICDISEASESCORE)## [1] 0.3006661##Poorly correlated (0.30) with their true value counterparts. MAE<-function(obs, pred){ mean(abs(obs-pred)) } MAE(ql_test$CHRONICDISEASESCORE,ql.p)## [1] 0.6313087## 0.6313 MAE(ql_test$CHRONICDISEASESCORE,mean(ql_test$CHRONICDISEASESCORE))## [1] 0.5834767## 0.5835 ##Regression tree model and OLS model serve different purposes. Regression Tree model classify predictors by conditions. For example, Charlson Score are split with options of Yes or No by MSA_Q_02, depending on score. Charlson Score of Less than 1 and MSA_Q_02 score of less han 4 have an average score of 0.4911. OLS estimates coefficient of variables which describe the relationship between the predictors and response variable.Try to use
M5Pto improve the model.
Sys.getenv("JAVA_HOME")## [1] "C:/Program Files (x86)/Java/jre1.8.0_361"Sys.setenv(JAVA_HOME="C:/Program Files (x86)/Java/jre1.8.0_361")
library(rJava)
library(RWeka)## Warning: package 'RWeka' was built under R version 4.2.3ql.m5 <- M5P(CHRONICDISEASESCORE~., data=ql_train)
ql.m5## M5 pruned model tree:
## (using smoothed linear models)
##
## CHARLSONSCORE <= 0.5 :
## | MSA_Q_01 <= 3.5 : LM1 (418/71.737%)
## | MSA_Q_01 > 3.5 : LM2 (142/90.248%)
## CHARLSONSCORE > 0.5 :
## | MSA_Q_02 <= 3.5 : LM3 (602/88.29%)
## | MSA_Q_02 > 3.5 :
## | | PH2_Q_02 <= 1.5 :
## | | | MSA_Q_06 <= 2.5 : LM4 (80/80.003%)
## | | | MSA_Q_06 > 2.5 : LM5 (46/81.21%)
## | | PH2_Q_02 > 1.5 : LM6 (203/111.651%)
##
## LM num: 1
## CHRONICDISEASESCORE =
## -0.2061 * LANGUAGE=SPANISH
## + 0.1008 * RACE_ETHNICITY=WHITE,AI-ALN,UNKNOWN,HISPANIC
## + 0.0045 * RACE_ETHNICITY=UNKNOWN,HISPANIC
## + 0.0054 * SEX=FEMALE
## + 0.091 * QOL_Q_02
## + 0.0033 * QOL_Q_06
## + 0.023 * QOL_Q_07
## - 0.0014 * QOL_Q_08
## - 0.0013 * QOL_Q_09
## + 0.0023 * MSA_Q_01
## + 0.0011 * MSA_Q_02
## - 0.0013 * MSA_Q_05
## + 0.0018 * MSA_Q_06
## - 0.0505 * MSA_Q_07
## - 0.0356 * MSA_Q_09
## - 0.0016 * MSA_Q_10
## - 0.032 * MSA_Q_14
## + 0.0633 * MSA_Q_17
## + 0.0007 * PH2_Q_01
## - 0.0018 * TOS_Q_02
## + 0.0031 * CHARLSONSCORE
## + 0.2525
##
## LM num: 2
## CHRONICDISEASESCORE =
## -0.0137 * LANGUAGE=SPANISH
## + 0.0083 * RACE_ETHNICITY=WHITE,AI-ALN,UNKNOWN,HISPANIC
## + 0.0045 * RACE_ETHNICITY=UNKNOWN,HISPANIC
## + 0.2377 * SEX=FEMALE
## + 0.0106 * QOL_Q_02
## + 0.1524 * QOL_Q_06
## + 0.0027 * QOL_Q_07
## - 0.0037 * QOL_Q_08
## - 0.0013 * QOL_Q_09
## + 0.0043 * MSA_Q_01
## + 0.0032 * MSA_Q_02
## - 0.0035 * MSA_Q_05
## + 0.005 * MSA_Q_06
## - 0.0029 * MSA_Q_07
## - 0.0036 * MSA_Q_09
## - 0.0841 * MSA_Q_10
## + 0.1118 * PH2_Q_01
## - 0.1096 * TOS_Q_01
## - 0.1042 * TOS_Q_02
## + 0.0031 * CHARLSONSCORE
## + 0.4688
##
## LM num: 3
## CHRONICDISEASESCORE =
## 0.0023 * RACE_ETHNICITY=WHITE,AI-ALN,UNKNOWN,HISPANIC
## + 0.2113 * RACE_ETHNICITY=UNKNOWN,HISPANIC
## + 0.0033 * SEX=FEMALE
## + 0.0938 * QOL_Q_02
## - 0.0425 * QOL_Q_04
## + 0.0426 * QOL_Q_06
## + 0.0009 * QOL_Q_07
## - 0.0647 * QOL_Q_09
## + 0.0412 * MSA_Q_01
## + 0.0008 * MSA_Q_02
## + 0.0004 * PH2_Q_01
## + 0.0008 * PH2_Q_02
## - 0.0013 * TOS_Q_02
## + 0.0019 * CHARLSONSCORE
## + 0.7686
##
## LM num: 4
## CHRONICDISEASESCORE =
## 0.0041 * RACE_ETHNICITY=WHITE,AI-ALN,UNKNOWN,HISPANIC
## + 0.0518 * RACE_ETHNICITY=UNKNOWN,HISPANIC
## + 0.028 * SEX=FEMALE
## + 0.0035 * QOL_Q_02
## - 0.0841 * QOL_Q_04
## + 0.0153 * QOL_Q_06
## + 0.0073 * QOL_Q_07
## + 0.1033 * QOL_Q_08
## - 0.0042 * QOL_Q_09
## + 0.0027 * MSA_Q_01
## + 0.0014 * MSA_Q_02
## + 0.0215 * MSA_Q_05
## + 0.0147 * MSA_Q_06
## - 0.0182 * MSA_Q_11
## + 0.008 * MSA_Q_13
## + 0.0084 * MSA_Q_14
## - 0.0058 * MSA_Q_15
## + 0.0004 * PH2_Q_01
## + 0.0015 * PH2_Q_02
## + 0.0098 * TOS_Q_01
## - 0.0108 * TOS_Q_02
## + 0.0019 * CHARLSONSCORE
## + 0.8506
##
## LM num: 5
## CHRONICDISEASESCORE =
## 0.0041 * RACE_ETHNICITY=WHITE,AI-ALN,UNKNOWN,HISPANIC
## + 0.0518 * RACE_ETHNICITY=UNKNOWN,HISPANIC
## + 0.028 * SEX=FEMALE
## + 0.0035 * QOL_Q_02
## + 0.0153 * QOL_Q_06
## + 0.0073 * QOL_Q_07
## - 0.0042 * QOL_Q_09
## + 0.0027 * MSA_Q_01
## + 0.0014 * MSA_Q_02
## - 0.0895 * MSA_Q_03
## + 0.3383 * MSA_Q_05
## + 0.0229 * MSA_Q_06
## - 0.0241 * MSA_Q_11
## + 0.008 * MSA_Q_13
## + 0.0084 * MSA_Q_14
## - 0.0058 * MSA_Q_15
## + 0.0004 * PH2_Q_01
## + 0.0015 * PH2_Q_02
## + 0.0098 * TOS_Q_01
## - 0.0108 * TOS_Q_02
## + 0.0019 * CHARLSONSCORE
## + 0.772
##
## LM num: 6
## CHRONICDISEASESCORE =
## 0.0041 * RACE_ETHNICITY=WHITE,AI-ALN,UNKNOWN,HISPANIC
## + 0.4092 * RACE_ETHNICITY=UNKNOWN,HISPANIC
## + 0.0199 * SEX=FEMALE
## + 0.0035 * QOL_Q_02
## + 0.2416 * QOL_Q_06
## + 0.0052 * QOL_Q_07
## - 0.0042 * QOL_Q_09
## + 0.086 * MSA_Q_01
## + 0.0014 * MSA_Q_02
## - 0.0805 * MSA_Q_04
## - 0.0822 * MSA_Q_11
## + 0.0051 * MSA_Q_13
## + 0.0055 * MSA_Q_14
## - 0.0037 * MSA_Q_15
## + 0.0004 * PH2_Q_01
## + 0.0015 * PH2_Q_02
## + 0.0063 * TOS_Q_01
## - 0.0076 * TOS_Q_02
## + 0.0019 * CHARLSONSCORE
## + 0.5968
##
## Number of Rules : 6summary(ql.m5)##
## === Summary ===
##
## Correlation coefficient 0.4914
## Mean absolute error 0.566
## Root mean squared error 0.7252
## Relative absolute error 94.0868 %
## Root relative squared error 87.1244 %
## Total Number of Instances 1491#Correlation coefficient 0.4914
#Mean absolute error 0.566
### M5 model has higher Correlation and lower MAE of than prediction tree. Thus the model is optimized.
ql.p.m5<-predict(ql.m5, ql_test)
summary(ql.p.m5)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.07583 0.69591 1.01151 1.01569 1.23885 2.56245cor(ql.p.m5, ql_test$CHRONICDISEASESCORE)## [1] 0.2998408#0.2998
MAE(ql_test$CHRONICDISEASESCORE, ql.p.m5)## [1] 0.6413623#0.641